Question: Simplify the following expression: $ k = \dfrac{1}{7} + \dfrac{5r - 5}{2r} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2r}{2r}$ $ \dfrac{1}{7} \times \dfrac{2r}{2r} = \dfrac{2r}{14r} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{5r - 5}{2r} \times \dfrac{7}{7} = \dfrac{35r - 35}{14r} $ Therefore $ k = \dfrac{2r}{14r} + \dfrac{35r - 35}{14r} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{2r + 35r - 35}{14r} $ $k = \dfrac{37r - 35}{14r}$